Up:

In Dublin, "up" a road or street is away from the sea or away from the river (thus, north and west if you are northside, south and west if you are southside). This seems to come quite naturally despite the fact that the city centre is pretty flat - people understand without thinking about it which is the "top" of Dawson Street", which way along O'Connell Street is "down", etc.

In Ireland, you go "up" to a bigger town or city, and "down to a smaller one. E.g. "I'm going down to Lanesboro for two weeks, but I'll come back up to Dublin for the weekend". An exception exists for travelling to Ulster, where the convention of North as "up" overrides the other rule - "I'm driving up to Belfast tomorrow".

Finally in rural areas a general convention of "up the road", for a house on the left, and "down the road", for a house on the right, is used, unless the road is obviously sloping.

All this by way of explanation that over here, "drop up to see me" can be used in all sorts of situations without any actual "up"!